They absolutely can get fleas, although it is rare because of the fact that they are inside pets and have such dense undercoats. Have you been offering you chin a dust bath regularly? I would dust him every other day (you can do it every day, but I worry about dry skin and itchiness that way). Is there fur loss? If there is you could have a ring-worm problem, and you need to see a vet immediately. Ringworm can be fatal to chins, and is transferable across species (you can get it, dogs and cats can get it, etc).
However, if it's fur biting only (although it doesn't sound like it) you wont be able to stop it completely. Some chins just chew their fur. My girl Dharma is a fur biter. We try to keep her busy and minimally stressed to MINIMIZE the amount of fur chewing she does, but she never completely stops the chewing. As long as she doens't have bald patches, or has chewed half her fur off, we figure it's just her little tick.
Regardless, it's sounding like it's Vet time for your little friend.
